Question

In the following exercises, expand each binomial using Pascal's Triangle.

$(z-3{)}^5$

Short answer

Expansion is$z^5-15z^4+90z^3-270z^2+405z-243$

Step-by-step solution

Step 1. Given Information 

Expand binomial using Pascal's Triangle.

$(z-3{)}^5$

Step 2. Solution

We have

Here the exponent is 5 hence we need to consider sixth row

The expansion is

$(z-3{)}^5=1z^5+5z^4(-3)+10z^3{(-3)}^2+10z^2{(-3)}^3+5z{(-3)}^4+1{(-3)}^5=z^5-15z^4+90z^3-270z^2+405z-243$